{"status": "success", "data": {"description_md": "Joy has $30$ thin rods, one each of every integer length from $1 \\text{ cm}$ through $30 \\text{ cm}$. She places the rods with lengths $3 \\text{ cm}$, $7 \\text{ cm}$, and $15 \\text{cm}$ on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?\n\n$\\textbf{(A)}\\ 16 \\qquad\\textbf{(B)}\\ 17 \\qquad\\textbf{(C)}\\ 18 \\qquad\\textbf{(D)}\\ 19  \\qquad\\textbf{(E)}\\ 20$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Joy has  <span class=\"katex--inline\">30</span>  thin rods, one each of every integer length from  <span class=\"katex--inline\">1 \\text{ cm}</span>  through  <span class=\"katex--inline\">30 \\text{ cm}</span> . She places the rods with lengths  <span class=\"katex--inline\">3 \\text{ cm}</span> ,  <span class=\"katex--inline\">7 \\text{ cm}</span> , and  <span class=\"katex--inline\">15 \\text{cm}</span>  on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 16 \\qquad\\textbf{(B)}\\ 17 \\qquad\\textbf{(C)}\\ 18 \\qquad\\textbf{(D)}\\ 19  \\qquad\\textbf{(E)}\\ 20</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "2017 AMC 12A Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12A_p07", "prev": "/problem/17_amc12A_p05"}}